Keywords: primary; 11B65; secondary; 05A10; Binomial coefficients; p-adic valuation; Lucas' theorem; Euler's totient theorem; Bernoulli numbers;
مقالات ISI (ترجمه نشده)
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Keywords: primary; 05A10; 05A19; 33C20; secondary; 11B65; 11B83; 11M06; Polygamma function; Integral representation; Logarithmic integral; Riemann zeta function;
Keywords: primary; 11A07; secondary; 05A10; 11B83; Congruences; Binomial coefficients; Harmonic numbers; Polylogarithms; Generating functions;
Keywords: primary; 11B65; secondary; 05A10; Binomial coefficient; Catalan triangle; Chu-Vandermonde convolution; Telescoping method; Partial binomial sum;
Keywords: primary; 81P70; 94B25; secondary; 05A10; 94B60; Quantum coding; Combinatorial codes;
Keywords: 52B45; 05A10; 52B20; 52A39; Combinatorial mixed valuations; Mixed volumes; Translation-invariant valuations; Combinatorial positivity; Discrete mixed volume;
Keywords: 15A03; 05A10; 05A17; Hyperinvariant subspaces; Characteristic subspaces; Generating polynomials; Combinatorics; Gaussian binomial coefficients;
Keywords: primary; 17C05; secondary; 05A10; 05C30; 15A69; 15B33; 16W10; 17-04; 17A30; 17A50; 17C50; 18D50; 20C30; 68R15; 68W30; Jordan algebras; Di- and tri-algebras; Pre- and post-Jordan algebras; Polynomial identities; Algebraic operads; Triplicators; Trisuccesso
Keywords: 05A10; 33F10; 68W30; Binomial sum; Multiple sum; Symbolic computation; Diagonal; Integral representation;
Keywords: Pascal triangle; Regular mosaics on hyperbolic plane; Hyperbolic planar tessellations11B99; 05A10
Keywords: primary; 11A63; 05A10; secondary; 11A25; Sum of digits; Base b representation; Factorial;
Keywords: primary; 11A05; 11A07; secondary; 05A10; 11B65; Binomial coefficients; Divisibility; WZ method;
Keywords: 05A10; 05A19Sign pattern matrices; Idempotence; Allow
Keywords: 11B83; 05A10; 11B65Multipartitional polynomials; Derivatives of polynomial sequences of multinomial type; Recursiveness relations
Keywords: 05A17; 05A10; 05A19; 05A20Binomial coefficients; Multinomial coefficients; Integer partitions
Keywords: 05A05; 05A10; 05A15; 05A19Trees; Posets; Parallelogram polyominoes; Tree-like tableaux; Bessel function; Permutations excedances
Half of a Riordan array and restricted lattice paths
Keywords: 05A05; 05A15; 05A10; 15A09; 15A36; Riordan array; Lukasiewicz path; Central coefficients; Catalan numbers; Generating function;
Ehrhart tensor polynomials
Keywords: 05A10; 05A15; 15A45; 15A69; 52B20; 52B45; Ehrhart tensor polynomial; hr-tensor polynomial; Pick's formula; Positive semidefinite coefficients; Half-open polytopes;
Arithmetic properties of Delannoy numbers and Schröder numbers
Keywords: primary; 11A07; 11B75; secondary; 05A10; 05A19; 11B65; 11C08; 33F99; Congruence; Polynomial; Delannoy number; Schröder number; Motzkin number;
Some determinants of path generating functions, II
Keywords: primary; 05A19; secondary; 05A10; 05A15; 11C20; 15A15; Hankel determinants; Catalan numbers; Ballot numbers; Motzkin numbers; Motzkin prefix numbers; Motzkin paths;
Proof of two conjectural supercongruences involving Catalan-Larcombe-French numbers
Keywords: primary; 11B65; 11B68; secondary; 05A10; 11A07; Central binomial coefficients; Supercongruence; Harmonic numbers;
The Rodriguez-Villegas type congruences for truncated q-hypergeometric functions
Keywords: primary; 11B65; secondary; 05A10; 05A30; Congruences; Truncated q-hypergeometric function; Cyclotomic polynomial; q-Chu-Vandermonde identity;
Identities involving weighted Catalan, Schröder and Motzkin paths
Keywords: primary; 05A15; secondary; 05A10; 05A19; Motzkin numbers; Catalan numbers; Narayana numbers; Schröder numbers; Weighted lattice paths; Bijection;
Some polynomials related to Dowling lattices and x-Stieltjes moment sequences
Keywords: 05A10; 05A20; 30B70; Dowling lattice; x-Stieltjes moment sequence; Continued fraction;
Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials
Keywords: primary; 05A10; 05A15; 11B37; 11B39; 11B68; 11B83; 11M35; 26C05; 26C10; secondary; 33C05; 34A99; 35A99; Generating functions; Functional equations; Partial differential equations; Hypergeometric functions; Hurwitz-Lerch zeta functions; Apostol-Bernoul
Supercongruences involving dual sequences
Keywords: primary; 11A07; 11B65; secondary; 05A10; 05A19; 11B68; 11B75; p-adic congruences; Binomial coefficients; Combinatorial identities; Dual sequences;
Applications of Riordan matrix functions to Bernoulli and Euler polynomials
Keywords: 05A05; 05A15; 15B36; 15A09; 05A30; 05A10; 05A19Riordan array; Riordan group; Pascal matrix; Bernoulli polynomials and numbers; Euler polynomials and numbers; Conjugate Bernoulli and Euler polynomials
Proof of a conjecture of Mircea Merca
Keywords: 05A10; 05A19; Multinomial coefficients; Binomial coefficients; Fine's formula;
On the families of q-Euler polynomials and their applications
Keywords: 05A10; 11B65; 11B68; 11B73Euler numbers and polynomials; q-Euler numbers and polynomials; Weighted q-Euler numbers and polynomials; Weighted q-Euler-Zeta function; p-adic q -integral on ZpZp
Supercongruences motivated by e
Keywords: primary; 11B65; secondary; 05A10; 11A07; 11B68; Supercongruences; Binomial coefficients; Bernoulli numbers;
Hankel determinant calculus for the Thue-Morse and related sequences
Keywords: 05A10; 05A15; 11B50; 11B65; 11B85; 11C20; 11J82; 11Y65; 15A15; 30B70; Hankel determinant; Continued fraction; Automatic sequence; Thue-Morse sequence; Stieltjes algorithm; Grafting technique; Chopping method;
On divisibility of sums of Apéry polynomials
Keywords: primary; 11A07; secondary; 11B65; 11B83; 05A10; Apéry polynomial; q-Lucas congruence;
Log-convexity of Aigner-Catalan-Riordan numbers
Keywords: 15A45; 05A20; 05A10; 15B36; 05A15; Log-convexity; TP2 matrix; Catalan-like number; Riordan array; Generating function;
Extended Bernoulli and Stirling matrices and related combinatorial identities
Keywords: 05A10; 05A19; 11B68; 11B73Bernoulli polynomials; Stirling numbers; Hyperharmonic numbers; Pascal matrix; Bernoulli matrix; Stirling matrix
Congruences involving (2kk)2(3kk)
Keywords: primary; 11A07; secondary; 33C45; 11E25; 11G07; 11L10; 05A10; 05A19; Congruence; Legendre polynomial; Character sum; Elliptic curve; Binary quadratic form;
Schröder matrix as inverse of Delannoy matrix
Keywords: 05A05; 05A15; 05A10; 15A09; 15A36; Delannoy number; Pascal matrix; Catalan number; Schröder number; Riordan array;
Symmetric recurrence relations and binomial transforms
Keywords: 05A19; 05A10; 11B68Recurrence relation; Binomial transform; Bernoulli numbers
Connections between p=x2+3y2 and Franel numbers
Keywords: primary; 11A07; 11E25; secondary; 05A10; 11B65; 11B75; Primes of the form x2+3y2; Franel numbers; Congruences;
A combinatorial proof of Shapiroʼs Catalan convolution
Keywords: 05A10; 05A19; Catalan numbers; Shapiro convolution;
Some q-congruences related to 3-adic valuations
Keywords: primary; 11B65; secondary; 05A10; 05A30; 11A07; 11S99; 3-adic valuation; Central binomial coefficient; Congruence; q-analogue;
Congruences arising from Apéry-type series for zeta values
Keywords: 11B65; 05A10; 11B68; 11A07; 33F10; 11B39; 11M06; Congruence; Creative telescoping; WZ pair; Finite central binomial sum; Multiple harmonic sum; Bernoulli number; Apéry-like series; Zeta value;
On Shapiroʼs Catalan convolution
Keywords: 05A10; 05A17; 05A30; Catalan numbers; Shapiro convolution; q-Hypergeometric series;
A new combinatorial identity for unicellular maps, via a direct bijective approach
Keywords: 05A19; 05A15; 05C30; 05A10; Polygon gluings; Bijection; Harer-Zagier numbers;
Some determinants of path generating functions
Keywords: primary; 05A19; secondary; 05A10; 05A15; 11C20; 15A15; Hankel determinants; Catalan numbers; Ballot numbers; Motzkin numbers; Motzkin paths; Non-intersecting lattice paths;
Generalized Levinson–Durbin sequences, binomial coefficients and autoregressive estimation
Keywords: 62M10; 05A10; 11B65Binomial coefficients; Generalized Levinson–Durbin sequence; Least squares estimator; Levinson–Durbin sequence; Partial correlations; Yule–Walker estimator
Factors of binomial sums from the Catalan triangle
Keywords: 05A10; 05A30; 11B65Catalan triangle; Divisibility; Chu–Vandermonde formula; Pfaff–Saalschütz identity; Lucas' theorem
A generalization of Calkin's identity
Keywords: 05A10; 05A15Omega operator; Combinatorial identity; Calkin's identity; Abel's summation rule
Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas
Keywords: 05A10; 05A30q-Binomial coefficient; q-Chu–Vandermonde formula; Euler's pentagonal number theorem; Lucas’ formulas
A discrete problem on d-dimensional symmetric weighted median filters
Keywords: 05A05; 05A10; 94A08; 94A12d-Dimensional symmetric weighted median filter; Root; Recurrent signal sequence
A factorization of the symmetric Pascal matrix involving the Fibonacci matrix
Keywords: 05A10; 11B39; 15A23Pascal matrix; Fibonacci matrix; Factorization of matrix